This a/r/tographic inquiry delves into questions about participatory art museum practice, specifically seeking to understand the nature of invitations to participate. Utilising drawings, writing and mapping of embodied participation, questions of how individuals are invited to participate in various locations and how these invitations inform the work of art museums that engage in participatory practice are considered. Conditions for participation, including familiarity, personalisation, enthusiasm, playfulness, narrative, uniqueness, sociability and listening, as well as anti-invitations that contradict moves toward participation, are discussed in relation to examples from the study and scholarly writing. The purpose of this article is twofold: first, to share research about participatory practice in various locations and its implications for art museums, and second, to explore the potential of arts-based research methodologies, particularly a/r/tography, for art museum education research.